The mint mark on Washington quarters dated 1932-1964 is on the reverse (tails) side below the eagle.
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1964 is the most common silver Washington quarter, it's worth about $3.00
Not all US coins have a "P" Mintmark. The 1944 Washington quarter with no mintmark was struck at the Philadelphia Mint. No US coin before 1979 struck at Philadelphi has a P mintmark except for the War Nickels of 1942-1945
No "S" mintmarks on a 1961 quarter, only a "D". The coin is valued for the silver, about $5.00.
Washington quarters dated before 1965 have the mint mark on the reverse (tails) side, near the bottom, just above the second letter "r" in the word "quarter."
Assuming it's worn from circulation, it would be worth around $3 for its silver content.